Cubic–Quartic Optical Soliton Perturbation with Differential Group Delay for the Lakshmanan–Porsezian–Daniel Model by Lie Symmetry

Sachin Kumar,Dalal Adnan Maturi,Simona Moldovanu,Luminita Moraru,Dalal H Al-Bogami,Hashim M Alshehri,Anjan Biswas,Yakup Yıldırım

doi:10.3390/sym14020224

Abstract

This paper employs Lie symmetry analysis to recover cubic–quartic optical soliton solutions to the Lakshmanan–Porsezian–Daniel model in birefringent fibers. The results are a sequel to the previously reported work on the same model in unpolarized fibers. Dark, singular, and straddled optical solitons that emerged from the scheme are presented.

Highlights

The concept of cubic–quartic (CQ) optical solitons emerged a couple of years ago out of extreme necessity when the chromatic dispersion (CD) effect ran low
This led to replenishing the low CD count with the CQ dispersive effect so that the necessary balance between CD and self-phase modulation (SPF) was sustained for the existence and propel of solitons for long distances through optical fibers
The generalized LPD model with arbitrary refractive index is considered via the Jacobi and Weierstrass elliptic functions in [2], where solitary waves corresponding to optical solitons are recovered for an arbitrary refractive index

Summary

Introduction

The concept of cubic–quartic (CQ) optical solitons emerged a couple of years ago out of extreme necessity when the chromatic dispersion (CD) effect ran low. The vector-coupled LPD equation in birefringent fibers was considered with the aid of the extended version of Jacobi’s elliptic function expansion scheme in [1], where Jacobi’s doubly periodic wave solutions are found. These solutions, in the limiting case, give rise to dark solitons, singular solitons or periodic solutions. Lie symmetry analysis, when applied, leads to coupled ordinary differential equations (ODEs) [14,15] These ODEs would be subsequently addressed using two powerful integration schemes: Kudryashov’s method and the improved F-expansion scheme. Αl , β l , γl , and λl are additional nonlinear effects

Lie Symmetry Analysis

Symmetry Reduction and Closed-Form Solutions

The Generalized Kudryashov’s Method

Improved F-Expansion Approach

Conclusions